In the application described here, light containing a range of wavelengths is dispersed and focused onto a photodiode array so that the output of the array is the spectrum. Typically the amount of light varies strongly with wavelength so that the pixels of the array generate photo charge at widely disparate rates.
A scan of the array is also made with the light blocked by a shutter to determine the dark current contribution and any offset due to the amplifying electronics. These dark values are subtracted to produce N digital values which measure the photo charge accumulated on each of the N pixels in time t0. A number of such scans are normally co-added so that an averaged set of dark-corrected pixel signals is created at some predetermined sample interval, or sample time.
Assuming that the light intensity falling on the diode array does not fluctuate, there are two sources of noise which degrade the precision of measuring the charge accumulated on each pixel. First there is shot noise, proportional to the square root of the accumulated charge. This is an unavoidable consequence of the discrete nature of electron flow. If this were the only noise source, the signal-to-noise ratio would improve as the square root of the amount of charge accumulated each time a pixel is read, and also as the square root of the number of times the pixel is read. Therefore, the signal-to-noise ratio would not depend on the exposure time t0, only on the rate of charge generation by the light. However, the second source of noise, so-called fixed noise, is independent of the light intensity, and corrupts the signal every time the pixel charge is read. It has two components: read noise, otherwise known as kTC noise, originating in the PDA device, and noise from the external amplifier. There is also a shot noise contribution from the pixel dark current, but at the relatively high light levels considered here it can be ignored.
If the light signal is high enough, shot noise dominates, which is proportional to the square root of the signal. But if the signal falls, the fixed noise dominates the signal-to-noise ratio, which now degrades in direct proportion to the falling signal.
In prior art methods it is standard practice to select the longest time period possible for t0 with the condition that none of the pixels saturate within the spectral range of interest for a particular experiment or series of measurements. The exposure time t0 is established by measuring the full spectrum with a reference material in the sample cell, using a short exposure time where it is known that no pixels will saturate. The exposure time t0 is then found by scaling the short exposure time so that the highest-signal pixel within the spectral range of interest will be, for example, 85% of saturation.
In the case of HPLC detection, the reference material is mobile phase at the start of a separation when no absorbing sample is present. Selecting t0 as long as possible minimizes the number of reads of the array within the sample time, thereby minimizing the effect of read noise added to the pixel signals. Pixels outside the spectral range of interest may saturate. The self-scanning process reads all of the pixels in the array at intervals of t0, and the values for those pixels outside the range of interest are simply ignored. Some of those pixels may saturate, but this does not affect data from pixels within the desired spectral range.
To optimize data collection and signal-to-noise ratio, exposure time t0 must be a sub-multiple of the sample time, which is the reciprocal of the data rate (i.e. the number of times per second the pixel values are reported). This condition assures that data collection is continuous, with no waiting periods when measurement time is lost.
Prior art approaches select the best exposure time t0 for the pixels with the highest signals, and the signal-to-noise ratio is optimized for these pixels. However other pixels in the array may receive much lower amounts of light and accumulate charge at a much lower rate. These pixels are read out with a large signal-to-noise disadvantage since the fixed noise associated with each read is constant, while the accumulated charge signal is low.